Overview

Goal is to assess the noise measurements from wayside single passby measurements in 2016-2021. In 2018, four pavement surface treatments were applied to test areas: 1/4" chip seal, 3/8" chip seal, Type II microsurfacing, and Type III microsurfacing.

There are eight sites, and four surface treatments; each surface treatment is replicated at two sites. Sound pressure levels were measured pre-treatment and post-treatment.

In the original assessment, the Type II microsurfacing was found to reduce overall sound intensity sound from OBSI measurements on average, from 99.2 to 97.6 dB. Other treatments did not reduce sound intensity levels, on average.

This analysis focuses on the wayside single passby data and assesses the effects of speed and pavement temperature in addition to surface treatments.

In the table below, SD_pavetemp is not applicable when the value is zero because the same pavement temperature was measured throughout the trial. These analyses exclude non-passenger car vehicle types (i.e., bus or motorcycle measurements), because they occurred infrequently and therefore vehicle type could not be used as a covariate in the analyses.

Summary of passby data collected by year and surface treatment
Year Treatment N autos Mean Speed (mph) Speed SD (mph) Mean Pavement Temp (deg F) Pavement Temp SD (deg F)
2016 Baseline - Chip Seal 93 53.47 7.13 95.59 4.99
2018 Type II Microsurfacing 27 45.36 5.55 124.16 1.27
2018 Type III Microsurfacing 16 51.24 9.61 69.26 3.84
2018 1/4 in Chip Seal 15 54.33 8.04 89.80 3.90
2018 3/8 in Chip Seal 30 45.53 6.58 119.00 0.00
2019 Type II Microsurfacing 34 45.09 6.34 66.76 16.02
2019 Type III Microsurfacing 14 56.04 5.61 81.00 0.00
2019 1/4 in Chip Seal 37 48.78 6.76 64.00 0.00
2019 3/8 in Chip Seal 34 43.76 6.08 85.00 0.00
2021 Type II Microsurfacing 33 45.68 6.25 79.15 6.50
2021 Type III Microsurfacing 32 50.36 6.85 97.24 1.36
2021 1/4 in Chip Seal 29 52.17 7.33 86.00 0.00
2021 3/8 in Chip Seal 29 44.21 5.31 74.93 4.28

2018 MANOVA Analysis with LZFeq

Using MANOVA, we see that there are strong effects of all the predictors on noise levels across the frequency spectra. The table shows the summary of the statistical test for the difference in sound pressure level (LZFeq) across all 1/3 octave bands attributable to each of the predictors: pavement temperature, speed, surface treatment, and the statistical interactions between temperature and speed, and between surface treatment and speed. All predictors were statistically significant, including the interactive effects of speed and temperature, and speed and surface treatment.

Pillai’s trace is a test statistic used in multivariate analyses. It is based on the eigenvalues associated with each predictor, across all 1/3 octave bands. A larger Pillai’s value indicates that this predictor explains more of the difference in the response data (the matrix of all 1/3 octave band LZFeq values). In order to interpret the statistical significance of this test statistic, we examine the p-value. This represents whether the test statistic is larger than expected by chance; a p-value less than 0.05 is considered statistically significant.

1/3 octave bands from 50 Hz to 20 kHz were used for this analysis.

Summary of MANOVA analysis for 1-month post-treatment (2018) compared to pre-treatment (2016)
Df Pillai approx F num Df den Df Pr(>F)
treatment 4 2.849 13.748 108 600 < 0.001
pavetemp 1 0.287 2.197 27 147 0.002
speed 1 0.683 11.755 27 147 < 0.001
pavetemp:speed 1 0.245 1.762 27 147 0.018
treatment:speed 4 1.058 1.998 108 600 < 0.001
Residuals 173

Post-hoc ANOVAs by LZFeq Frequency

Plotting ANOVA LZFeq change from pre-treatment.

Response variables: treatment, pavement temperature, and speed, as well as the interactions between treatment and speed, as well as pavement temperature and speed.

The plots are generated from the output of the statistical models, holding pavement temperature constant at 90 degrees and speed constant at 50 mph. The change in LZFeq is calculated as the difference between the predicted sound levels at 90 degrees and 50 mph for a particular treatment, compared to the baseline pavement conditions in 2016 in the same conditions. The error bars are the standard errors for predicted LZFeq values.

The predicted values at these conditions are saved as LZFeq_2018_ANOVA_PredictedVals.csv and LZFeq_2018_ANOVA_PredictedVals_StdErr.csv

The plots below became Figure 18 in the DEVA QPP 1 month report.

Plotting standardized curves

The following shows the predicted LZFeq levels at standardized pavement temperature (90 degrees) and vehicle speed (50 mph). Two versions are shown, a point plot and a ‘ribbon plot’. Both show the predicted values, +/- 1 standard error.

The second plot is interactive; clicking on the legend will show or hide a specific treatment.

2019 MANOVA Analysis with LZFeq

For the 2016 to 2019 comparison, all predictors remained significant, except that the interaction between pavement temperature and speed became only marginally significant (p = 0.076). The variable is retained here for comparison with the previous analysis of 2016 to 2018 data.

Summary of MANOVA analysis for 1-year post-treatment (2019) compared to pre-treatment (2016)
Df Pillai approx F num Df den Df Pr(>F)
treatment 4 2.383 10.315 108 756 < 0.001
pavetemp 1 0.223 1.982 27 186 0.004
speed 1 0.685 14.946 27 186 < 0.001
pavetemp:speed 1 0.175 1.461 27 186 0.076
treatment:speed 4 0.707 1.502 108 756 0.001
Residuals 212

Post-hoc ANOVAs by LZFeq Frequency

Plotting ANOVA change in LZFeq from pretreatment, comparing 2019 measurements to 2016.

Response variables: treatment, pavement temperature, and speed, as well as the interactions between treatment and speed, as well as pavement temperature and speed.

The plots are generated from the output of the statistical models, holding pavement temperature constant at 90 degrees and speed constant at 50 mph. The change in LZFeq is calculated as the difference between the predicted sound levels at 90 degrees and 50 mph for a particular treatment, compared to the baseline pavement conditions in 2016 in the same conditions. The error bars are the standard errors for predicted LZFeq values.

The predicted values at these conditions are saved as LZFeq_2019_ANOVA_PredictedVals.csv and LZFeq_2019_ANOVA_PredictedVals_StdErr.csv

The plots below became figure 29-32 in the DEVA QPP 1 year report.

Plotting standardized curves

The following shows the predicted LZFeq values at standardized pavement temperature (90 degrees) and vehicle speed (50 mph). Two versions are shown, a point plot and a ‘ribbon plot’. Both show the predicted values, +/- 1 standard error.

The second plot is interactive; clicking on the legend will show or hide a specific treatment.

2021 MANOVA Analysis with LZFeq

Measured data can be affected by vehicle speed, pavement type, pavement temperature, and the interactions between these main effects. In order to further isolate the effect of pavement type, a Multiple Analysis of Variance (MANOVA) was conducted using measurements from the pre-treatment and post-treatment conditions. The predictors in the MANOVA include the surface treatment, vehicle speed, and pavement temperature. The response variables are the one-third octave band levels associated with the pass-by for each event. In contrast to an ANOVA model, the response in the statistical model is a matrix (number of observations × number of one-third octave bands as response variables) rather than a single vector (number of observations × 1 response variable). This analysis allows the greatest amount of data to be utilized in order to isolate the contribution of pavement type on the difference in measured levels.

Model selection was conducted to determine the most parsimonious MANOVA model with the fewest predictive parameters that would explain the most change in the response variable matrix. An array of concise models containing a unique subset of the predictor variables was evaluated against a model containing all predictors. The full list of predictors includes the main effects (i.e., surface treatment, vehicle speed, and pavement temperature) and interaction effects (i.e., statistical interaction between vehicle speed and pavement temperature, as well as the interaction between surface treatment and vehicle speed). Partial F-statistics were computed to compare each concise model against the full model, in which a large and significant F-statistic indicates that the concise model fails to capture a significant amount of variance in the response data due to the deleted predictive parameters. The statistical significance of the partial F-statistic is determined based on the p-value. For this analysis, a p-value less than 0.05 is considered statistically significant. This threshold corresponds to a 95% likelihood that the measured differences in LZFeq data for each passby are attributable to the predictor variables in the full model, and did not occur simply by chance. As shown in (Table 5 in the 3-year measurement report), all concise models containing a subset of the predictors produced significant partial F-statistics with p-values below 0.05, meaning the full model containing all predictor variables is the best model to use for the statistical analysis.

The table (Table 6 in the 3-year measurement report) shows the summary of the MANOVA statistical test for the difference in sound pressure level (LZFeq) across all 1/3 octave bands attributable to each of the predictors. Note that only 1/3 octave bands from 50 Hz to 4 kHz were included in this analysis. The high frequency analysis limit is due to the internal noise floor of the measurement equipment, which results in poor signal to noise ratio at high frequencies in areas with low ambient noise, such as Death Valley. The first column in the table displays the parameters being evaluated for their impact on the matrix of LZFeq 1/3 octave band data measured for each passby. The parameters being evaluated in this data set include either a main effect (surface treatment, vehicle speed, and pavement temperature) or an interaction effect (statistical interaction between vehicle speed and pavement temperature, as well as the interaction between surface treatment and vehicle speed). The second column shows the number of degrees of freedom associated with each parameter, which indicates the number of unique options that can vary. The third column is an estimate of Pillai’s trace, which is a test statistic used in multivariate analyses to evaluate the predictive power of each parameter. A larger Pillai’s value indicates that the parameter is responsible for a greater portion of the difference in spectral LZFeq observed between each passby. In order to interpret the statistical significance of this test statistic, we examine the p-value, which is shown in the final column of the table. For this analysis, a p-value less than 0.05 is considered statistically significant. This threshold corresponds to a 95% likelihood that the measured differences in LZFeq data for each passby are attributable to the predictor variable, and did not occur simply by chance. The other columns in the table display the approximate F-statistic, (another means of evaluating the statistical significance of predictor variables in which a higher value indicates a greater impact on the response data), and the degrees of freedom for the numerator and denominator in the F-statistics.

The MANOVA indicates that there are strong, statistically significant effects on the noise levels across the frequency spectra for most predictors included in the analysis. All predictors are statistically significant at a level of \(\alpha\)=0.05 except for the interactive effect of vehicle speed and pavement temperature, as the p-value of Pillai’s test statistic is greater than 0.05. Surface treatment and vehicle speed are the strongest independent predictors of noise, as they both have large Pillai values with corresponding p-values less than 0.001. The latter can be interpreted as a greater than 99% chance that the LZFeq difference measured between passbys can be confidently attributed to surface treatment and vehicle speed.

Summary of MANOVA analysis for 3-years post-treatment (2021) compared to pre-treatment (2016)
Df Pillai approx F num Df den Df Pr(>F)
treatment 4 1.623 6.556 80 768 < 0.001
speed 1 0.546 11.363 20 189 < 0.001
pavetemp 1 0.193 2.265 20 189 0.002
speed:pavetemp 1 0.131 1.428 20 189 0.113
treatment:speed 4 0.51 1.402 80 768 0.015
Residuals 208

Post-hoc ANOVAs by LZFeq Frequency

Once the statistical significance of the MANOVA was established, it was appropriate to conduct single Analyses of Variance (ANOVAs) for each one-third octave band frequency using this model to determine the effects of each parameter on sound level.

The below plots (figures 42-45 in the 3-year report) illustrate the current difference in spectral LZFeq from pre-treatment, after three years of use. The plots are generated from the output of the ANOVA models based on 2021 measured data, holding vehicle speed constant at 50 mph and pavement temperature constant at 90 degrees Fahrenheit to isolate the effect of the surface treatments. The change in LZFeq after three years is calculated as the difference between the predicted sound levels at 50 mph and \(90^{\circ}F\) for a particular treatment in 2021, compared to the baseline pavement conditions in 2016 under the same vehicle speed and pavement temperature conditions. The predicted values and standard errors at these conditions are saved as LZFeq_2021_ANOVA_PredictedVals.csv and LZFeq_2021_ANOVA_PredictedVals_StdErr.csv

Note that in these figures the error bars are based on ± 1 standard error, which provides a confidence interval of 68.3%, rather than the typical ± 1.96 standard errors, which provides a 95% confidence interval. This was done to help highlight potential differences. Because this interval is less conservative, as new data are added, some trends may change. From these figures, the following conclusions can be drawn:

  • The 3/8" chip seal pavement attenuates more high frequency content but less mid frequency content than the pre-treatment, older 3/8" chip seal pavement.
  • Similar to the results after one year, the type III microsurfacing after three years of use still attenuates less low frequency content than the pre-treatment pavement baseline.

Plotting standardized curves

The following shows the predicted LZFeq values at standardized vehicle speed (50 mph) and pavement temperature ( \(90^{\circ}F\)). Two versions are shown, a point plot and a ‘ribbon plot’. Both show the predicted values, +/- 1 standard error.

The second plot is interactive; clicking on the legend will show or hide a specific treatment.